The Adahessian is a sophisticated optimization algorithm tailored for use with TensorFlow. It is designed to enhance traditional first-order optimization techniques, such as Adam, by integrating second-order information through the Hessian trace, which is approximated using Hutchinson's method. This incorporation allows Adahessian to adaptively scale learning rates for each parameter, making it particularly effective for challenging, non-convex optimization problems.

Key Features

• Adaptive Learning Rates: Leverages curvature information from the loss surface to improve parameter adaptation.
• Advanced Parameter Control: Includes adjustable parameters such as learning rate, weight decay, and Hessian scaling which facilitate fine-tuning of model training.

Parameters:

• learning_rate (float): Initialize the learning rate (default: 0.1).
• beta1 (float): Decay rate for the first moment estimates used in the optimization (default: 0.9).
• beta2 (float): Decay rate for the second moment estimates concerning Hessian approximations (default: 0.999).
• epsilon (float): Small constant included to avoid division by zero (default: 1e-8).
• Additional parameters enable features such as weight decay, clipping gradients, and using Exponential Moving Average (EMA) for model weights.

Usage Example

Integrating Adahessian into a training workflow is straightforward. Below is a sample code demonstrating its implementation:

import tensorflow as tf

# Define model and loss function
model = tf.keras.Sequential([...])
loss_fn = tf.keras.losses.MeanSquaredError()

# Initialize the Adahessian optimizer
optimizer = Adahessian(
    learning_rate=0.01, 
    beta1=0.9, 
    beta2=0.999, 
    weight_decay=0.01
)

# Define the training step function
@tf.function
def train_step(x, y, model, optimizer):
    with tf.GradientTape(persistent=True) as tape:
        predictions = model(x, training=True)
        loss = loss_fn(y, predictions)
        gradients = tape.gradient(loss, model.trainable_variables)
    optimizer.apply_gradients(zip(gradients, model.trainable_variables), tape)

# Execute the training loop
for epoch in range(epochs):
    for x_batch, y_batch in dataset:
        train_step(x_batch, y_batch, model, optimizer)

The Adahessian optimizer offers a robust solution for optimizing models in TensorFlow, providing both enhanced performance through adaptive learning rates and comprehensive parameter control.